Where do these figures come from?...anybody? ...and in fact if mathematically calculated in some shape or form, I would expect that none of these figures are as accurate across the board as they could be.

Perhaps the queen is worth 8.75... and the knight worth 3.25, and the rook 5.25 and when considering an exchange of queen for a good knight and rook I should give it more attention?... Are two rooks really better than a queen?... Is it worth exchanging both bishops for knights if I can get a pawn out of it?

Of course the value of pieces change as the game progresses, not ever sure to what extent this will vary.

But does anybody got any unusual systems or ideas for calculating material value of this sort of thing?

adrianallen
24 ( +1 | -1 )I think these are just guidesThe importance of a piece and it value very much depends on the position. Having a material advantage, but a passive position, you'll probably still lose.

Generally 2 rooks are better than a queen, particularly if on same rank or row, but not always.

anaxagoras
73 ( +1 | -1 )Your list of piece values is like a fan in a vaccum. For one thing, the half point extra value of a Bishop vs a Knight is dubious. Sometimes a Knight is worth *at least as much, if not more* than a Bishop. Personally, I find that most players vastly overrate the value of Bishops to Knights, and will seek to exchange their Knights for Bishops regardless of the position. Granted, in a wide open position, the Bishop is superior. But even in a semi-open position, any purported difference in value is not clear.

If you want to be accurate, derive a table of values in different sorts of positions, e.g.

maca
55 ( +1 | -1 )Mathematical correctnessI have read that most of these normal values base in pieces mathematical mobility, all but knight; knight's mathematical mobility is much less than bishops's, but it gets bonus in closed positions so that it's often rated equal with bishop.

Notice, of course, that passed pawn can be as valuable as a full queen.

MaCa

Ps. i consider a bishop bit more powerful than a knight, becouse i like open positions.

Dont know really what I can get out of this discussion, but just curious, I might get some insight into this...

but VERY often we (I) make decisions on strategy largely based on the material score (probably more than any other factor, like space, time and king safety ).

So if based on mathematical mobility...

Would it be correct to say a pawn that has not moved is worth more than 1 point?

Does this factor in that a bishop can only visit half the squares of the board, whilst a knight can visit all? (typically for endgame knight is definately worth more in this scenario... although it has to be said a mutually supporting bishop and pawn in end game is extremely untouchable in my experience.)

Would it be true to say that an uncastled rook is worth more than a castled one?

Can a King have a material score as an attacking piece?... ( I often divide the board into two, left and right to get a material score to get ideas where and when it is good to attack/defend.... and to measure space I divide the board the other way and emasuer occupied an attacked squares.)

Fire away if you can add anything to this, but I just reckon the typical chess players material scoring isnt as scientific and accurate as it could be.

finduriel
214 ( +1 | -1 )hmmwhy would an uncastled rook be worth more than a castled one? Usually a castled rook is much more active than an uncastled. Rooks don't do much on their original square other than defend the pawn in front of them and whatever they can reach on the last rank.

Well, about Knights and Bishops. I think it was Steinitz who said that the way to fight Knights is to take away their "advanced support points." A Knight on the sixth rank and on a centre file, guarded by a pawn and not attackable by any of the opponent's pawns is usually much superior to any Bishop, simply because it restricts the opponent so much. You should check out some games by Kasparov who loves to advance his Knights. A classic example would be Karpov-Kasparov: r2qr1k1/5ppp/p4n2/1pbP1bB1/8/N1Nn1B2/PP1Q1PPP/3R1RK1 w - - 0 17

I don't know if you can read Forsyth notation, but you can find an introduction to it here: www.eudesign.com/chessops/basics/cpr-notf.htm The immensely strong black Knight on d3 dominates the whole board while White's bishops don't really do much. White's Rooks cannot access the open files because the Knight rules over both e1 and c1. This provides two good entry points for the Black Rooks.

According to J. Silman, the Bishop-Knight "imbalance" is often the deciding factor in a game. If you have a Knight for a Bishop, you should find a good position for it and try to keep the position from opening up. If you have a Bishop for a Knight, take away the Knight's "advanced support points" (on your third and fourth file) and try to open up the position.

Try and get a copy of Silman's _The Amateur's Mind_ and go through the Rosenthal-Steinitz game (pp41ff in the 2nd ed.), for example. Very instructive!

Dividing the board is a bit complicated. Bishops often control more squares on the side they're _not_ on. The biggest material advantage on one side doesn't help much if there's nothing to attack (consider the Benko gambit where Black has an almost empty queenside).

superblunder
147 ( +1 | -1 )SpurtusI think you are confused about 'Mobility'. A piece's intrinsic value is based on that piece's mobility. Everyone knows that the queen is better than all the other pieces...why? Because intrinsically a queen is by far the most mobile of pieces. If however the queen is trapped behind its own pawns and pieces, say on a corner square with two pawns and a knight surrounding it, the queen is temporarily totally immobilized and if the opponent's queen is active during this time, the player with the immobilized queen will be at a serious, if not losing disadvantage. The queen is still intrinsically valuable because it has the potential of getting out of it's corner and becoming very powerful again. The key to strong positional strategy is to mobilize your forces making them as active as possible while playing to restrict your opponent's forces. Pawns are handled a little different because of their slow, ever-forward pace. Indeed proper pawn play is one of the most difficult parts of chess to master, entire books have been written on the subject of pawn strategy.

I also recommend Silman's books. If you are interested in finding a very lengthy answer to your question concerning material value, the best piece I have ever read concerning this is in a book by Jonathan Tisdall called "Improve Your Chess Now." In it is a chapter entitled 'the Value of The Pieces', And I think you will find it very enlightening.

caldazar
90 ( +1 | -1 )The older piece values were arried at through the experiences of old masters. Specifically, past players just felt that the various pieces were of certain values relative to one another. More recently, IM Larry Kaufman conducted a statistical study of a large database of games to attempt to more accurately determine these average values. I don't recall what numbers Kaufman came up with, but he did publish an article on his findings so you can probably dig up the article if you're really motivated.

I doubt Kaufman did a statistical study of the relative value of the king, but as an attacking piece, it's generally considered to be slightly superior to a knight or bishop but inferior to a rook.

In the end, though, these average values are not terribly useful (in my opinion anyway) because they are simply averages and do not necessarily reflect the true value of the piece as it exists as part of a particular chess position.

These values, i remember, were calculated in empty board, so i really can't say if castled rook is worse than uncastled.

Also, this "mobility" meaned the ammount of squares the piece can get from some other square of the board(the position was noticed; in the middle, edge, or corner) with one move(if the board is empty), so the pawn's positon won't affect to it's mobility in any way(the double step with first move was noticed).

mester
7 ( +1 | -1 )Numbers, numbers all depending on a specific position. Not much more to add.

mate_you_in_fifty
28 ( +1 | -1 )yup...These numbers all depend on the position. The king can be more powerless than a pawn in the middlegame if surrounding squares are controlled by enemy pieces. But at close range amongst uncoordinated enemy pieces in the endgame (leaving out the queen!),the king may be as powerful as a rook. It all depends.

atrifix
58 ( +1 | -1 )The most interesting alternate material value system that I've seen is enumerated in Lasker's Manual of Chess, and seems to be more or less accurate. Andy Soltis wrote an article on it in Chess Life about a year ago. Chess, however, is not a game of mathematics, and so trying to compare positions solely by adding up the "values" of the pieces is usually meaningless.

The king is *generally* worse than a rook in the endgame because of its short-range mobility, but usually valued as better than a minor piece because of its ability to reach surrounding squares.

spurtus
90 ( +1 | -1 )Number number and more numbersIt is correct and I agree, to say ( as most have mentioned ) that the value of pieces individually or collectively is all based on position...

... A king might be 5, a bad bishop might be 2.9... whatever...

...but at the crux of my desires to attain a smidgen more chess knowledge is... what is the accurate accepted mathematical mean value of pieces... from which I can THEN modify the material score based on whether its a good pawn, bad pawn, trapped knight etc. etc...

I seek this information in order to weigh up a position perhaps more accurately, maybe one day it will give me a slight advantage... dont really know... but.... I just find it hard to just accept values like 1,3,3.5,5,9, Somebody HAS rounded them... or thought it irrelevant to be more accurate???

I'd just like to know how accurate it is this mean/median/average that we generally accept and use...

Cheers and thanks for input so far, Spurtus.

superblunder
41 ( +1 | -1 )Once again.Chess is not a numerical game. The pieces DO NOT have a numerical value...You will gain far more knowledge by playing experience than any table of numerical piece values. Are two minor pieces better than a rook and pawn? Are two rooks better than a queen and pawn? Is a bishop better than a knight? Numbers won't answer those questions...studying and playing chess will.

bogg
134 ( +1 | -1 )superblundermakes a valid point. One of the hardest concepts that I have ever tried to teach was the exchange sacrifice. I will demonstrate this by trying to recall a conversation about a position where I was trying to lead someone to an exchange sacrifice of their Ra1 for their opponent's Bg7.

Me: So, what are you trying to do in this position? Friend: I have a big lead in development and a lot of pressure against his King. I am playing for a direct attack. Me: Good! What is your opponent's best defensive piece? Friend: His Bg7, if I could remove it he would be toast. Me: Good! Now what is your worst offensive piece? Friend: My Ra1, it doesn't enter into the attack at all. Me: Great! Now how do you think you should proceed with your attack? Friend: Well, he is attacking my Ra1 with his Bg7 so first I have to move it .... The above dialogue was looped through about 4 times when my friend sat bolt upright on the last question and answered that he should sac the exchange. While this was the answer that I was hoping for I still do not like the phrasing. He wasn't sacrificing anything, he was allowing his opponent to exchange his opponent's best piece for his worst piece and when he recaptured with his queen he also gained a couple of tempos for his attack. That doesn't sound like a sacrifice to me!

I understand how material 'value' can be insignificant in many circumstances, but I dont believe that the game is THAT pure...

... can you put your hand on your heart and say you never ever think something in numerical terms?... consider exchanges/compensation/attacking strategy.

I can't, subliminally the whole concept of material advantage is ticking over in the back of my brain... I'll usually consider myself up in the game if I have exchanged a bishop for the opponents rook, and will want to take the game to end game at quickly as possible with this advantage.

Sorry to keep boring you,

Spurtus.

mate_you_in_fifty
33 ( +1 | -1 )of courseI'm sure everyone has thought of material values at some time or another. You see,you wanted to take the game to endgame with your advantage because that's where the disparity in power is most evident. In the middlegame it's more important which piece is taking part in an attack or other important goal.

atrifix
96 ( +1 | -1 )GenerallyI do not think in mathematical terms with the sole exception of counting how many pawns there are. If, for example, I am winning an exchange, the first question is whether my opponent can get compensation for the exchange, and whether the compensation is enough, not the number of "points" that there are. Finishing the game usually consists of limiting the opponent's compensation and eventually realizing the potential of the pieces. Alternatively, if I lose 2 pieces but force my opponent's king to e4, I'm liable to stop keeping track of the number of pieces altogether.

Of course, the first thing everyone learns after the moves and rules is the value system 1-3-3-5-9, but what is often lost in translation is that these are just supposed to give you a general feel for the relative value of the pieces. Trying to compare whether a rook and two pawns is better than two pieces by using the comparison 7>6 is both misguiding and detrimental, especially because in most positions two pieces are better than a rook and two pawns.

bogg
68 ( +1 | -1 )spurtusI agree that being up material is usually a good thing. What I was getting at is that a piece has a specific value because of how effective it is now and its prospects for the future. I find it much easier to reason through a position by realizing that my knight is better than my opponents rook than trying to see that I have so much compensation that the value of my pieces plus my compensation out weighs that of my opponent's pieces even though I am down an exchange. For me at least it is a lot easier to find positional sacrifices when I keep in mind how the pieces compare to each other in the position in question than to try and weigh a myriad of positional factors.

anaxagoras
109 ( +1 | -1 )"I understand how material 'value' can be insignificant in many circumstances, but I dont believe that the game is THAT pure... ... can you put your hand on your heart and say you never ever think something in numerical terms?... consider exchanges/compensation/attacking strategy."

Well, being the hack that I am, the first thing I often do is calculate: space, time, and material. After I acheive a result I have a *hint* as to how to evaluate the position. Of course material is important, and so are numerical terms, but the real error is to believe that material is the *only* numerical term (not to believe that numerical terms have no meaning for chess). Numerical calcuation has a small ammount of utility in positional analysis; it is at best something to start with and at worst a dead metaphor.

"I can't, subliminally the whole concept of material advantage is ticking over in the back of my brain..."

I hear you there. What ruins my chess more than anything else is an early concern for gaining material in lieu of more important positional goals. Live and learn I guess.

nobarakskaoneb
44 ( +1 | -1 )units valuesAssigning the Pawn with one point, the values of other pieces were also assigned: 3 points each for Bishop and Knight, 5 points for Rook, 9 points for Queen.

3 points for Bishop, for example, is equivalent to saying that a Bishop is usually worth 3 pawns.

These values of pieces and pawn arent just assigned by 'feeling'. It was actually the result of immense research on the powers of pieces and pawns in the ending.

caldazar
45 ( +1 | -1 )"These values of pieces and pawn arent just assigned by 'feeling'. It was actually the result of immense research on the powers of pieces and pawns in the ending. "

They were? I certainly missed that research then. Who did the research and where did the researcher(s) write up their findings? The only research of this type I'm aware of is the stastistical study done by Kaufman a few years back, and he studied all phases of the game, not just endings.

dozer
53 ( +1 | -1 )Experience...I would say that the relative material values of the pieces are mostly valuable to beginners, but as a player progresses he should take in to consideration the values of the position. Like the activity of pieces and pawn structure, weak and strong squares and such. Only then one can a**es the position correctly whether White is better or Black in a given position if some exchanges of pieces are made. Experience helps here alot...